When a node has been requested for consideration, it appears on the list of Nodes to consider. Each node is listed as it would appear on the Front Page, with
the addition of the following between the title bar and the body of the node:

four radio buttons, labeled 'keep', 'edit', 'reap', and 'nada' (the default).

Keep

Don't modify in any way. Leave it alone.

Edit

Suggest the OP (or the Janitors) clean up the posting as described by the consideration text.

At the bottom of the page is a 'submit' button.
Friars (and above) can mark a vote on each consideration request.

Once you have voted on a consideration of a node, the radio buttons are replaced with
the current tally of 'keep', 'edit', and 'reap' votes, and you can no longer vote
on that consideration. Note that submitting your ballot with 'nada' checked doesn't
count as a vote on that consideration.

Each request should be carefully considered. This means actually reading the node!
If you are in doubt as the proper disposition of the consideration, check 'nada'.
Also reflect on whether you ought to recuse yourself from the vote (for example,
if you are the node author). Remember, if you vote 'nada', you can always come back
and vote on the consideration later. See How do I use the power of consideration responsibly?

If the voting on a consideration goes preponderantly toward edit (according to a magical formula of the keep/edit/reap tally), the node gets added to the list of "nodes requiring editing". This brings it to the attention of the janitors, who may then take action, as described in What do Janitors do?. Remember, however, that janitors are never obliged to perform the change, no matter how the voting goes!

If the voting on a consideration goes preponderantly toward reap (again, according to a magical formula of the keep/edit/reap tally), the node will be automatically reaped. Note, though, that the conditions under which this happens are quite stringent, the idea being that it's better to err on the side of not reaping a bad node, rather than reaping a good node.
See What is Reaping? for more detail.